The federal government should withhold infrastructure funding until the states demonstrate they are cracking down on building industry criminality, according to a growing group of crossbenchers pushing the government to go further on the CFMEU.

The intervention comes as the Fair Work Commission is expected to apply to the Federal Court for the appointment of independent administration to the embattled union.

The federal government directed the commission to take control of the union in July, following a string of reports linking it to criminal gangs and standover tactics.

Newly sworn-in Industrial Relations Minister Murray Watt said earlier this week that work on the appointment of an administrator to the CFMEU was ongoing. A government source told the ABC on Thursday the application would be made "very soon".

The timing is a matter for the commission.

In the meantime, Labor is preparing snap legislation to counter any potential CFMEU appeal if the federal court approves the administrator.

Crossbench anger over government response

Several crossbenchers have written to the prime minister saying the federal government's efforts to date against the union are merely a "short-term fix" that won't address the law-breaking they claim is driving up building costs, contributing to inflation, and eroding economic productivity.

The push includes independent MPs Allegra Spender, Kate Chaney, Kylea Tink, Monique Ryan, Zali Steggall and Zoe Daniel, as well as senator Jacqui Lambie, who are all demanding an "urgent meeting" with the prime minister.

"Commonwealth money shouldn't be going to states until they show they are dealing with these issues on the ground, particularly in Victoria where there was an awareness about what was going on but a complete lack of action," Ms Spender told the ABC.

"Why should we be paying for things when we're not getting value for money and seeing potential criminality on sites?"

Labor has suspended the union and banned donations to the party.

Ongoing calls for greater action against the union and building sector more broadly could become a flash point when parliament returns this month from the winter break.

Crossbench letter warns of 'corruption' and 'contagion'

In a letter to the prime minister obtained by the ABC, the crossbench group slammed the government for failing to establish "an appropriate replacement body" when it last year abolished the Australian Building and Construction Commission (ABCC), a watchdog established by the Coalition.

While some members of the group voted last year to abolish the ABCC, they argue they had little choice as the measure was included in an omnibus bill that had other industrial relations changes they supported.

Ms Spender, who voted against and was critical of the abolition of the watchdog, said the government has "no credible alternative" to address issues in the sector.

While the ABCC was not perfect, she said the broader construction industry problems have been "kicking around for 20 years".

"Politics as usual has completely failed to deliver an outcome.

"At the same time, productivity is down 30 per cent, while costs are going up."

The crossbench group told the prime minister that legitimate businesses are too intimidated by the actions of the CFMEU to speak out.

"I've talked to contractors that say: 'I will never go on the record, I will never say anything publicly because I know my business can be destroyed if the CFMEU decides to take action against me,'" Ms Spender said.

The group said the industry's failings were a "sort of corruption" that was having a corrosive effect throughout the community.

"The lack of accountability has led to organised crime finding its way to capture public money and creates significant risk of contagion into other sectors of the economy," they said.

Independent senator David Pocock, who did not sign the letter, has also called for more scrutiny of the sector and voiced frustration about the abolition of the ABCC.